Finite Group Databasebeta

← #11808207

Subgroups — #11808207

Order 1152.

2832 conjugacy classes of subgroups.

The subgroup lattice has 501 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3830C211yesmaximal, characteristic, complemented
2C2×#64102C211yesmaximal, characteristic, complemented
3C2×#64090C212yesmaximal, complemented
4C32×#394C211yesmaximal, characteristic, complemented
5#10592922C211yesmaximal, characteristic, complemented
6#10592678C211yesmaximal, characteristic, complemented
7#10592659C212yesmaximal, complemented
8#10592658C212yesmaximal, complemented
9C22⋊C4×C3⋊Dic3C212yesmaximal, complemented
10#10592372C211yesmaximal, characteristic, complemented
11#10592365C211yesmaximal, characteristic, complemented
12#76889—34nomaximal
13C22×C32×D4C2211yescharacteristic
14C22×#638C2212yes—
15C22×#638C2212yes—
16C23×C3⋊Dic3C2212yes—
17C2×#3830—28no—
18C2×#3830—24no—
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic
22C22×#634C2211yescharacteristic
23C2×C32×C4⋊C4C2211yescharacteristic
24C2×C32×C22⋊C4C2212yes—
25C2×C32×C22⋊C4C2212yes—
26C2×#3757C2212yes—
27C2×#3752C2212yes—
28C2×#3752C2212yes—
29C2×#3752C2211yescharacteristic
30C2×#3752C2211yescharacteristic
31C2×#3750C2212yes—
32C2×C4×C3⋊Dic3C2212yes—
33C2×C4×C3⋊Dic3C2211yescharacteristic
34#64102—24no—
35#64090—28no—
36C32×#95C2211yescharacteristic
37#63658C2211yescharacteristic
38#63658C2212yes—
39#63658C2212yes—
40C22×#237—34no—
41C2×#893—34no—
42C2×#67⋊C4—38no—
43C3×#394D314yescomplemented
44#5223—34no—
45#4979—34no—
46#4960—38no—
47#4959—38no—
48Dic3×C22⋊C4—38no—
49#4673—34no—
50#4666—34no—
51C24×C32C2312yes—
52C23×C3⋊D3C2311yescharacteristic
53C23×C3⋊D3C2311yescharacteristic
54C2×C32×D4—24no—
55C2×C32×D4—22no—
56C22×C32×C4C2311yescharacteristic
57C22×C32×C4C2312yes—
58C22×C32×C4C2311yescharacteristic
59C22×C32×C4C2311yescharacteristic
60C2×#638—24no—
61C2×#638—24no—
62C2×#638—24no—
63C2×#638—24no—
64C2×#638—24no—
65C2×#638—24no—
66C22×C3⋊Dic3—24no—
67C22×C3⋊Dic3—24no—
68C22×C3⋊Dic3D418yescomplemented
69C22×C3⋊Dic3C2311yescharacteristic
70C22×C3⋊Dic3C2312yes—
71C22×C3⋊Dic3C2312yes—
72C22×C3⋊Dic3C2311yescharacteristic
73#3830—232no—
74C2×C4⋊(C3⋊D3)—22no—
75C2×C4⋊(C3⋊D3)—22no—
76C2×C4⋊(C3⋊D3)—22no—
77C2×C4×C3⋊D3—24no—
78C2×C4×C3⋊D3—24no—
79C2×C4×C3⋊D3—22no—
80C2×C4×C3⋊D3D414yescomplemented
81C2×#634—22no—
82C2×#634—24no—
83C32×C4⋊C4—22no—
84C32×C22⋊C4—24no—
85C32×C22⋊C4—24no—
86#3757—24no—
87#3752—22no—
88#3752—22no—
89#3752—24no—
90#3752—24no—
91#3750—24no—
92C4×C3⋊Dic3—24no—
93C4×C3⋊Dic3—22no—
94#2388—91noSylow
95C22×C3×D4C2×D314yes—
96C22×#67—38no—
97C22×#67—38no—
98C23×Dic3—38no—
99C2×#237—616no—
100C2×#237—632no—
101C22×D12—34no—
102C22×C4×D3—34no—
103C22×C4×D3—34no—
104C22×Dic6—34no—
105C2×C3×C4⋊C4C2×D314yes—
106C2×C3×C22⋊C4C2×D318yes—
107C2×C3×C22⋊C4C2×D318yes—
108C2×#217—38no—
109C2×(C2×D3)⋊C4—38no—
110C2×(C2×D3)⋊C4—38no—
111C2×(C2×D3)⋊C4—34no—
112C2×(C2×D3)⋊C4—34no—
113C2×Dic3⋊C4—38no—
114C2×C4×Dic3—38no—
115C2×C4×Dic3—34no—
116#893—616no—
117#67⋊C4—632no—
118C3×#95C2×D314yes—
119C3⋊#95—34no—
120C3⋊#95—38no—
121C3⋊#95—38no—
122C23×C32—22no—
123C23×C32—22no—
124C23×C32—22no—
125C23×C32—22no—
126C23×C32—22no—
127C23×C32—22no—
128C23×C32C2×D414yes—
129C23×C32C2411yescharacteristic
130C22×C3⋊D3—21no—
131C22×C3⋊D3—22no—
132C22×C3⋊D3—22no—
133C22×C3⋊D3—22no—
134C22×C3⋊D3—21no—
135C22×C3⋊D3—21no—
136C22×C3⋊D3—21no—
137C22×C3⋊D3—22no—
138C22×C3⋊D3C2×D412yes—
139C22×C3⋊D3#4112yescomplemented
140C32×D4—28no—
141C2×C32×C4—21no—
142C2×C32×C4—22no—
143C2×C32×C4—21no—
144C2×C32×C4—22no—
145C2×C32×C4—22no—
146C2×C32×C4—21no—
147C2×C32×C4—22no—
148C2×C32×C4—22no—
149C2×C32×C4C2×D412yes—
150C2×C32×C4#4112yescomplemented
151#638—216no—
152#638—216no—
153C2×C3⋊Dic3—22no—
154C2×C3⋊Dic3—22no—
155C2×C3⋊Dic3—22no—
156C2×C3⋊Dic3—22no—
157C2×C3⋊Dic3—216no—
158C2×C3⋊Dic3—21no—
159C2×C3⋊Dic3—22no—
160C2×C3⋊Dic3C2×D414yes—
161C2×C3⋊Dic3C2×D414yes—
162C2×C3⋊Dic3C2×D412yes—
163C2×C3⋊Dic3#4114yescomplemented
164C4⋊(C3⋊D3)—28no—
165C4×C3⋊D3—28no—
166C4×C3⋊D3—44no—
167#634—28no—
168C22×#41—91no—
169C2×C4×D4—91no—
170C2×C4×D4—92no—
171#395—91no—
172#394—92no—
173#394C3⋊D311yescharacteristic, complemented
174#393—91no—
175#392—91no—
176#392—92no—
177C4×C22⋊C4—92no—
178C4×C22⋊C4—91no—
179C24×C3C22×D318yes—
180C23×D3—34no—
181C23×D3—34no—
182C2×C3×D4—216no—
183C2×C3×D4—28no—
184C22×C3×C4C22×D318yes—
185C22×C3×C4C22×D314yes—
186C22×C3×C4C22×D314yes—
187C22×C3×C4C22×D314yes—
188C2×#67—616no—
189C2×#67—616no—
190C2×#67—616no—
191C2×#67—616no—
192C2×#67—616no—
193C2×#67—616no—
194C22×Dic3—34no—
195C22×Dic3—332no—
196C22×Dic3—38no—
197C22×Dic3—38no—
198C22×Dic3—34no—
199C22×Dic3—616no—
200C22×Dic3—616no—
201#237—6128no—
202C2×D12—68no—
203C2×D12—68no—
204C2×D12—68no—
205C2×C4×D3—316no—
206C2×C4×D3—616no—
207C2×C4×D3—616no—
208C2×C4×D3—68no—
209C2×Dic6—616no—
210C2×Dic6—68no—
211C3×C4⋊C4—28no—
212C3×C22⋊C4—216no—
213C3×C22⋊C4—216no—
214#217—616no—
215(C2×D3)⋊C4—616no—
216(C2×D3)⋊C4—616no—
217(C2×D3)⋊C4—68no—
218(C2×D3)⋊C4—68no—
219Dic3⋊C4—616no—
220C4×Dic3—616no—
221C4×Dic3—68no—
222C22×C32—24no—
223C22×C32—24no—
224C22×C32—24no—
225C22×C32—42no—
226C22×C32—42no—
227C22×C32—42no—
228C22×C32—42no—
229C22×C32C22×D411yescharacteristic
230C22×C32C22×D412yes—
231C22×C32C2×#4111yescharacteristic
232C22×C32C2×#4111yescharacteristic
233C22×C32C2×#4112yes—
234C2×C3⋊D3—22no—
235C2×C3⋊D3—22no—
236C2×C3⋊D3—22no—
237C2×C3⋊D3—24no—
238C2×C3⋊D3—22no—
239C2×C3⋊D3—41no—
240C2×C3⋊D3—42no—
241C2×C3⋊D3—41no—
242C2×C3⋊D3—42no—
243C2×C3⋊D3—42no—
244C32×C4—22no—
245C32×C4—22no—
246C32×C4—41no—
247C32×C4—42no—
248C3⋊Dic3—24no—
249C3⋊Dic3—24no—
250C3⋊Dic3—41no—
251C3⋊Dic3#12014yes—
252C2×#41—188no—
253C2×#41—184no—
254C22×Q8—91no—
255C22×D4—92no—
256C22×D4—92no—
257C22×D4—91no—
258C22×D4C2×C3⋊D311yescharacteristic
259C23×C4—92no—
260C23×C4—91no—
261C23×C4—91no—
262C4×D4—188no—
263C4×D4—184no—
264C2×C4⋊C4—92no—
265C2×C4⋊C4C2×C3⋊D311yescharacteristic
266C2×C22⋊C4—92no—
267C2×C22⋊C4—92no—
268C2×C22⋊C4—91no—
269C2×C22⋊C4—91no—
270C2×C22⋊C4—92no—
271C2×C22⋊C4C2×C3⋊D312yes—
272C2×C22⋊C4C2×C3⋊D312yes—
273C2×C42—92no—
274C2×C42—91no—
275#95—91no—
276#95—92no—
277#95—92no—
278#95C2×C3⋊D311yescharacteristic
279C23×C3—28no—
280C23×C3—28no—
281C23×C3—28no—
282C23×C3—28no—
283C23×C3—28no—
284C23×C3—28no—
285C23×C3D3×D4116yes—
286C23×C3C23×D314yes—
287C22×D3—38no—
288C22×D3—38no—
289C22×D3—64no—
290C22×D3—68no—
291C22×D3—68no—
292C22×D3—64no—
293C22×D3—64no—
294C22×D3—68no—
295C22×D3—64no—
296C22×D3—68no—
297C3×D4—232no—
298C2×C3×C4—24no—
299C2×C3×C4—28no—
300C2×C3×C4—24no—
301C2×C3×C4—28no—
302C2×C3×C4—28no—
303C2×C3×C4—24no—
304C2×C3×C4—28no—
305C2×C3×C4—28no—
306C2×C3×C4D3×D418yes—
307C2×C3×C4#23718yescomplemented
308#67—664no—
309#67—664no—
310C2×Dic3—38no—
311C2×Dic3—316no—
312C2×Dic3—316no—
313C2×Dic3—316no—
314C2×Dic3—664no—
315C2×Dic3—68no—
316C2×Dic3—68no—
317C2×Dic3—68no—
318C2×Dic3—68no—
319C2×Dic3—64no—
320C2×Dic3—68no—
321D12—632no—
322C4×D3—632no—
323C4×D3—1216no—
324Dic6—632no—
325C2×C32—44no—
326C2×C32C2×#12011yescharacteristic
327C2×C32#52512yes—
328C2×C32#52511yescharacteristic
329C2×C32#53211yescharacteristic
330C2×C32#53212yes—
331C3⋊D3—42no—
332C3⋊D3—42no—
333C24—91no—
334C24—91no—
335C24C22×C3⋊D312yes—
336#41—1832no—
337C2×Q8—184no—
338C2×Q8—182no—
339C2×D4—24no—
340C2×D4—22no—
341C2×D4—182no—
342C2×D4—182no—
343C2×D4—184no—
344C2×D4—184no—
345C2×D4—184no—
346C2×D4—184no—
347C2×D4—184no—
348C2×D4—184no—
349C2×D4—182no—
350C22×C4—91no—
351C22×C4—92no—
352C22×C4—92no—
353C22×C4—98no—
354C22×C4—94no—
355C22×C4—91no—
356C22×C4—184no—
357C22×C4—184no—
358C22×C4—182no—
359C22×C4—184no—
360C22×C4—184no—
361C22×C4C22×C3⋊D312yes—
362C22×C4C22×C3⋊D311yescharacteristic
363C22×C4C22×C3⋊D311yescharacteristic
364C22×C4C22×C3⋊D311yescharacteristic
365C4⋊C4—22no—
366C4⋊C4—184no—
367C22⋊C4—24no—
368C22⋊C4—24no—
369C22⋊C4—184no—
370C22⋊C4—184no—
371C22⋊C4—182no—
372C22⋊C4—184no—
373C22⋊C4—182no—
374C42—182no—
375C42—184no—
376C22×C3—216no—
377C22×C3—216no—
378C22×C3—216no—
379C22×C3—48no—
380C22×C3—48no—
381C22×C3—48no—
382C22×C3—48no—
383C22×C3C2×D3×D418yes—
384C22×C3C2×D3×D414yes—
385C22×C3C2×#23714yes—
386C22×C3D3×#4114yes—
387C22×C3D3×#4118yes—
388C2×D3—616no—
389C2×D3—68no—
390C2×D3—68no—
391C2×D3—68no—
392C2×D3—68no—
393C2×D3—128no—
394C2×D3—124no—
395C2×D3—124no—
396C2×D3—128no—
397C2×D3—128no—
398C3×C4—28no—
399C3×C4—28no—
400C3×C4—44no—
401C3×C4—48no—
402Dic3—316no—
403Dic3—616no—
404Dic3—616no—
405Dic3—124no—
406C32#238811yescharacteristic, complemented, Sylow
407C23—22no—
408C23—22no—
409C23—22no—
410C23—22no—
411C23—22no—
412C23—22no—
413C23—92no—
414C23—92no—
415C23—182no—
416C23—181no—
417C23—182no—
418C23—181no—
419C23—181no—
420C23—182no—
421C23—182no—
422C23—181no—
423C23D4×C3⋊D314yes—
424C23C23×C3⋊D311yescharacteristic
425Q8—188no—
426D4—28no—
427D4—188no—
428D4—1816no—
429D4—1816no—
430C2×C4—21no—
431C2×C4—22no—
432C2×C4—21no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—21no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—94no—
439C2×C4—92no—
440C2×C4—94no—
441C2×C4—94no—
442C2×C4—188no—
443C2×C4—1816no—
444C2×C4—182no—
445C2×C4—182no—
446C2×C4—182no—
447C2×C4—182no—
448C2×C4—181no—
449C2×C4—182no—
450C2×C4—364no—
451C2×C4D4×C3⋊D312yes—
452C2×C4#383012yescomplemented
453C2×C3—416no—
454C2×C3D3×#12014yes—
455C2×C3#559618yes—
456C2×C3#560614yes—
457C2×C3#565618yes—
458C2×C3#566814yes—
459D3—128no—
460D3—128no—
461C22—24no—
462C22—24no—
463C22—24no—
464C22—42no—
465C22—42no—
466C22—42no—
467C22—42no—
468C22—184no—
469C22—182no—
470C22—182no—
471C22—182no—
472C22—182no—
473C22—362no—
474C22—361no—
475C22—361no—
476C22—362no—
477C22—362no—
478C22C2×D4×C3⋊D312yes—
479C22C2×D4×C3⋊D311yescharacteristic
480C22C2×#383011yescharacteristic
481C22#41×C3⋊D311yescharacteristic
482C22#41×C3⋊D312yes—
483C4—22no—
484C4—22no—
485C4—41no—
486C4—42no—
487C4—94no—
488C4—184no—
489C4—184no—
490C4—361no—
491C3#7688914yescomplemented
492C2—44no—
493C2—362no—
494C2—362no—
495C2C3⋊D3×#12011yescharacteristic
496C2#1059606712yes—
497C2#1059607711yescharacteristic
498C2#1059612712yes—
499C2#1059613911yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
FittingC32×#394C2
hypercenter#394C3⋊D3
hypocenterC32#2388
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #394

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#3830C2semidirect
2. C2×#64102C2semidirect
3. C2×#64090C2semidirect
4. C32×#394C2semidirect
5. #10592922C2semidirect
6. #10592678C2semidirect
7. #10592659C2semidirect
8. #10592658C2semidirect
9. C22⋊C4×C3⋊Dic3C2semidirect
10. #10592372C2semidirect
11. #10592365C2semidirect
43. C3×#394D3semidirect
68. C22×C3⋊Dic3D4semidirect
80. C2×C4×C3⋊D3D4semidirect
139. C22×C3⋊D3#41semidirect
150. C2×C32×C4#41semidirect
163. C2×C3⋊Dic3#41semidirect
173. #394C3⋊D3semidirect
307. C2×C3×C4#237semidirect
406. C32#2388semidirect
452. C2×C4#3830semidirect
491. C3#76889semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#38302
C2×#641022
C2×#640902
C32×#3942
#105929222
#105926782
#105926592
#105926582
C22⋊C4×C3⋊Dic32
#105923722
#105923652
#768893